Signal recovery via compressive sensing
Compressed Sensing (CS) has applications in many areas of signal processing such as data compression, data acquisition and dimensionality reduction. CS ensures faithful recovery of certain signals or images using a small number of samples or observations than traditional methods use. Many n...
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Format: | Theses and Dissertations |
Language: | English |
Published: |
2015
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Online Access: | http://hdl.handle.net/10356/65166 |
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Institution: | Nanyang Technological University |
Language: | English |
Summary: | Compressed Sensing (CS) has applications in many areas of signal processing such as data
compression, data acquisition and dimensionality reduction. CS ensures faithful recovery of
certain signals or images using a small number of samples or observations than traditional
methods use. Many natural signals have sparse representations when expressed in a proper basis.
Sparse signal can be recovered from the observation vector using convex optimization
teclmiques like !!-minimization (Basis Pursuit). For a faster recovery, greedy algorithms such as
Orthogonal Matching Pursuit (OMP), Regularized Orthogonal Matching Pursuit (ROMP), Stagewise
Orthogonal Matching Pursuit (St- OMP), Backtracking-based Adaptive Orthogonal
Matching Pursuit (BAOMP), etc. can be used . In my experiments OMP algoritlun is used to
recover the original signal as it less complex and computationally inexpensive.
The initial part of the project deals with understanding the recovery of sum of sine/cosine waves
via compressive sensing using OMP algorithm by applying proper basis functions so that signal
is represented with good sparsity. The second and third part of the project is aimed at recovering
sine wave using different basis functions like DCT , DFT and WARPED DFT. This was
challenging because there were multiple peaks and spectral leakages in the frequency spectrum
which imposed difficulty while recovering the data with few measurements. The last part of the
project involved recovering twin sine wave which was also challenging because of less
frequency separation between two sine waves. This imposed problems while picking the location
of the peak from the projection matrix ofOMP.
This report shows the different plots of Mean Squared Error versus Number of Measurements
for different basis functions which helps in determining the best basis function that can be
applied to given signal so that the signal becomes nearly sparse or exactly sparse and can be
recovered with less number of measurements. |
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